Complexes PR #2: changes to a first set of packages

M2/Macaulay2/packages/CellularResolutions.m2

@@ -28,7 +28,7 @@ export {--types
         "cellLabel",
         "hullComplex",
         "isCycle",
-        "isFree",
+--        "isFree",
         "isMinimal",
         "isSimplex",
         "newCell",
@@ -42,8 +42,8 @@ export {--types
         "CellDimension",
         "InferLabels",
         "LabelRing",
-        "Reduced",
-        "Prune"
+        "Reduced"
+        --"Prune"
         }
 protect labelRing
 protect label
@@ -418,17 +418,17 @@ boundaryMap(ZZ,CellComplex) := opts -> (r,cellComplex) -> (
     sparseBlockMap(codomain,domain,new HashTable from L)
     );
 
-chainComplex(CellComplex) := {Reduced=>true, Prune=>true} >> o -> (cellComplex) -> (
-    if not cellComplex.cache.?chainComplex then (
-        cellComplex.cache.chainComplex =
-            (chainComplex apply(max((dim cellComplex) + 1,1), r -> boundaryMap(r,cellComplex)))[1]
+complex(CellComplex) := {Reduced=>true, Prune=>true} >> o -> (cellComplex) -> (
+    if not cellComplex.cache.?complex then (
+        cellComplex.cache.complex =
+            (complex apply(max((dim cellComplex) + 1,1), r -> boundaryMap(r,cellComplex)))[1]
         );
     ret := if not o.Reduced then (
-        Ccopy := chainComplex apply(max cellComplex.cache.chainComplex,
-                                    i -> cellComplex.cache.chainComplex.dd_(i+1));
+        Ccopy := complex apply(max cellComplex.cache.complex,
+                                    i -> cellComplex.cache.complex.dd_(i+1));
         Ccopy
         )
-        else cellComplex.cache.chainComplex;
+        else cellComplex.cache.complex;
     if o.Prune then (
         prune ret --how expensive is prune? should it be cached?
         )
@@ -437,16 +437,16 @@ chainComplex(CellComplex) := {Reduced=>true, Prune=>true} >> o -> (cellComplex)
 
 --Get homology directly from cell complex
 homology(ZZ,CellComplex) := opts -> (i,cellComplex) -> (
-    homology_i chainComplex(cellComplex)
+    homology_i complex(cellComplex)
     );
 
 homology(CellComplex) := opts -> (cellComplex) -> (
-    homology chainComplex(cellComplex)
+    homology complex(cellComplex)
     );
 
 --Get cohomology directly from cell complex
 cohomology(ZZ,CellComplex) := opts -> (i,cellComplex) -> (
-    cohomology_i Hom(chainComplex(cellComplex),cellComplex.labelRing^1)
+    cohomology_i Hom(complex(cellComplex),cellComplex.labelRing^1)
     );
 
 ----------
@@ -516,7 +516,7 @@ facePoset(CellComplex) := (cellComplex) -> (
 -- Minimality
 -------------
 
-isFree = method(TypicalValue => Boolean);
+--isFree = method(TypicalValue => Boolean);
 --check if all the labels are free modules
 isFree(CellComplex) := (cellComplex) -> (
     R := cellComplex.labelRing;

M2/Macaulay2/packages/CellularResolutions/doc.m2

@@ -51,7 +51,7 @@ doc ///
             This class represents a single cell in a cell complex. A cell has
             a boundary, a dimension, and a label. In most cases, the label should
             be a monomial. But the cells in this package may be anything.
-            However for functions such as @TO chainComplex@ to work, the labels
+            However for functions such as @TO complex@ to work, the labels
             should be either monomials, ideals, or modules.
             In the monomial case, we can view the label as a module by taking
             the submodule generated by the monomial in the ring. There should be
@@ -541,21 +541,20 @@ doc ///
             d2 = boundaryMap_2 C
             assert(d1*d2==0)
     SeeAlso
-        (chainComplex,CellComplex)
-        (chainComplex,SimplicialComplex)
+        (complex,CellComplex)
+        (complex,SimplicialComplex)
 ///
 
 doc ///
     Key
-        (chainComplex,CellComplex)
+        (complex,CellComplex)
         Reduced
-        [(chainComplex,CellComplex),Reduced]
-        Prune
-        [(chainComplex,CellComplex),Prune]
+        [(complex,CellComplex),Reduced]
+        [(complex,CellComplex),Prune]
     Headline
         compute the cellular chain complex for a cell complex
     Usage
-        chainComplex C
+        complex C
     Inputs
         C : CellComplex
             the cell complex for which to compute the chain complex
@@ -564,7 +563,7 @@ doc ///
         Prune => Boolean
             that controls whether the modules in the chain complex are pruned
     Outputs
-        : ChainComplex
+        : Complex
             the dimension of the complex
     Description
         Text
@@ -573,15 +572,15 @@ doc ///
             cell complex will be a complex of modules over the ring
             associated to the cell complex.
             By default, the option "Reduced" is set to true, so
-            the resulting ChainComplex has a rank 1 free module in homological degree -1.
+            the resulting Complex has a rank 1 free module in homological degree -1.
         Example
             R = QQ[x]
             a = newSimplexCell({},x);
             b1 = newCell {a,a};
             b2 = newCell {a,a};
             C = cellComplex(R,{b1,b2});
-            chainComplex C
-            chainComplex(C,Reduced=>false)
+            complex C
+            complex(C,Reduced=>false)
         Text
             For details see Combinatorial Commutative Algebra Section 4.1.
             If we restrict to the case of monomial labels, then, subject to
@@ -601,8 +600,8 @@ doc ///
             eyz = newSimplexCell({vy,vz});
             f = newSimplexCell({exy,exz,eyz});
             C = cellComplex(R,{f});
-            betti chainComplex(C)[-1]
-            assert(betti chainComplex(C)[-1] == betti res I);
+            betti complex(C)[-1]
+            assert(betti complex(C)[-1] == betti res I);
         Text
             The option "Prune," also defaulted to true, controls whether the modules in the complex
             are pruned before being returned. With the "Prune" option set to the default of true,
@@ -614,11 +613,11 @@ doc ///
             b = newSimplexCell({},y);
             e = newCell {a,b};
             C = cellComplex(R,{e});
-            chainComplex C
-            chainComplex(C,Prune=>false)
+            complex C
+            complex(C,Prune=>false)
     SeeAlso
         (boundaryMap,ZZ,CellComplex)
-        (chainComplex,SimplicialComplex)
+        (complex,SimplicialComplex)
         (homology,CellComplex)
         (homology,ZZ,CellComplex)
         (cohomology,ZZ,CellComplex)
@@ -664,7 +663,7 @@ doc ///
             prune oo
     SeeAlso
         (homology,ZZ,CellComplex)
-        (chainComplex,CellComplex)
+        (complex,CellComplex)
 ///
 
 doc ///
@@ -712,7 +711,7 @@ doc ///
     SeeAlso
         (homology,CellComplex)
         (cohomology,ZZ,CellComplex)
-        (chainComplex,CellComplex)
+        (complex,CellComplex)
 ///
 
 doc ///
@@ -756,7 +755,7 @@ doc ///
     SeeAlso
         (homology,CellComplex)
         (homology,ZZ,CellComplex)
-        (chainComplex,CellComplex)
+        (complex,CellComplex)
 ///
 
 doc ///
@@ -920,7 +919,6 @@ doc ///
 
 doc ///
     Key
-        isFree
         (isFree,CellComplex)
     Headline
         checks if the labels of a cell complex are free modules
@@ -1134,7 +1132,7 @@ doc ///
         Example
             S = cellComplexSphere(QQ,3)
             cells(S)
-            chainComplex S
+            complex S
             prune homology S
     SeeAlso
         cellComplexRPn
@@ -1238,12 +1236,12 @@ doc ///
             S = QQ[x,y,z];
             I = monomialIdeal (x^2*z, x*y*z, y^2*z, x^3*y^5, x^4*y^4, x^5*y^3);
             H = hullComplex I
-            chainComplex H
+            complex H
             cells(1,H)/cellLabel
             cells(2,H)/cellLabel
             isMinimal H
             H2 = hullComplex (3/2,I)
-            prune HH chainComplex H2
+            prune HH complex H2
     SeeAlso
         (taylorComplex,MonomialIdeal)
 ///
@@ -1271,7 +1269,7 @@ doc ///
             S = QQ[x,y,z];
             I = monomialIdeal (x^2, y^2, z^2);
             T = taylorComplex I
-            C = chainComplex T
+            C = complex T
             C.dd
     SeeAlso
         (hullComplex,MonomialIdeal)
@@ -1300,7 +1298,7 @@ doc ///
             S = QQ[x,y,z];
             I = monomialIdeal (x^2*z, x*y*z, y^2*z, x^3*y^5, x^4*y^4, x^5*y^3);
             C = scarfComplex I
-            chainComplex C
+            complex C
             cells(1,C)/cellLabel
             cells(2,C)/cellLabel
             isMinimal C

M2/Macaulay2/packages/CellularResolutions/tests.m2

@@ -6,7 +6,7 @@ assert(isWellDefined e);
 assert(dim e === -infinity);
 assert(#maxCells e == 0);
 assert(#maxCells skeleton(0,e) == 0);
-chainComplex e;
+complex e;
 ///
 
 
@@ -27,10 +27,10 @@ assert(l1=!=l2);
 assert(dim l1==1);
 assert(dim l2==1);
 C = cellComplex(QQ,{l1,l2});
-CchainComplex = chainComplex C;
-assert(HH_0(CchainComplex)==0);
-assert(prune HH_1(CchainComplex)==QQ^1);
-assert(HH_2(CchainComplex)==0);
+Ccomplex = complex C;
+assert(HH_0(Ccomplex)==0);
+assert(prune HH_1(Ccomplex)==QQ^1);
+assert(HH_2(Ccomplex)==0);
 f1 = newCell {l1,l2};
 C = cellComplex(QQ,{f1});
 assert(dim C==2);
@@ -48,11 +48,11 @@ assert(rank source del2 == 1);
 assert(rank target del2 == 2);
 assert(rank del2 == 1);
 assert(del100 == map(QQ^0,QQ^0,{}));
-CchainComplex = chainComplex C;
-assert(HH_0(CchainComplex)==0);
-assert(HH_1(CchainComplex)==0);
-assert(HH_2(CchainComplex)==0);
-assert(HH C == HH CchainComplex);
+Ccomplex = complex C;
+assert(HH_0(Ccomplex)==0);
+assert(HH_1(Ccomplex)==0);
+assert(HH_2(Ccomplex)==0);
+assert(HH C == HH Ccomplex);
 assert(isFree(C));
 ///
 
@@ -63,11 +63,11 @@ l = newCell {v,v};
 f = newCell {(l,1),(l,1)};
 C = cellComplex(ZZ,{f});
 assert(dim C===2);
-prune HH chainComplex C
+prune HH complex C
 assert(HH_0 C == 0);
-assert(homology(0,chainComplex(C,Reduced=>false))==ZZ^1);
-assert(homology(1,chainComplex(C,Reduced=>false))==ZZ^1/(2*ZZ^1));
-assert(HH_1 chainComplex C == cokernel matrix {{2}})
+assert(homology(0,complex(C,Reduced=>false))==ZZ^1);
+assert(homology(1,complex(C,Reduced=>false))==ZZ^1/(2*ZZ^1));
+assert(HH_1 complex C == cokernel matrix {{2}})
 assert(HH^2 C == cokernel matrix {{2}});
 assert(HH^1 C == 0);
 assert(dim skeleton_1 C == 1);
@@ -82,11 +82,11 @@ assert(dim D == 1);
 assert(isSimplex a);
 assert(not isSimplex b1);
 assert(not isSimplex b2);
-DchainComplex = chainComplex D;
-assert(HH_0(DchainComplex)==0);
+Dcomplex = complex D;
+assert(HH_0(Dcomplex)==0);
 R = ring D;
-assert(prune HH_1(DchainComplex)==R^2);
-assert(HH_2(DchainComplex)==0);
+assert(prune HH_1(Dcomplex)==R^2);
+assert(HH_2(Dcomplex)==0);
 ///
 
 
@@ -133,7 +133,7 @@ lxz = newSimplexCell({vx,vz});
 fxyz = newSimplexCell({lxy,lyz,lxz});
 assert(cellLabel fxyz === x*y*z);
 D = cellComplex(R,{fxyz});
-C = (chainComplex D);
+C = (complex D);
 assert(HH_(-1)(C)==cokernel matrix {{x,y,z}});
 assert(C.dd^2==0);
 assert(degrees C_0 == {{1}, {1}, {1}});
@@ -150,7 +150,7 @@ lyz = newSimplexCell({vy,vz});
 lxz = newSimplexCell({vx,vz});
 fxyz = newSimplexCell({lxy,lyz,lxz});
 D = cellComplex(R,{fxyz});
-C = (chainComplex D)[-1];
+C = (complex D)[-1];
 assert(HH_0(C)==R^1/module ideal(x,y,z))
 assert(HH_1(C)==0)
 assert(C.dd^2==0);
@@ -167,7 +167,7 @@ lyz = newSimplexCell {vy,vz};
 lxz = newSimplexCell {vx,vz};
 fxyz = newSimplexCell {lxy,lyz,lxz};
 D = cellComplex(R,{fxyz});
-C = (chainComplex D)[-1];
+C = (complex D)[-1];
 assert(C.dd^2==0);
 assert(not isFree(D));
 ///
@@ -210,7 +210,7 @@ assert(# cells(3,C)==1);
 assert(HH_1(C)==0);
 assert(HH_2(C)==0);
 assert(HH_3(C)==0);
-assert((chainComplex C).dd^2==0);
+assert((complex C).dd^2==0);
 C1 = skeleton(1,C);
 assert(dim C1 == 1);
 assert(rank HH_1 C1 == 5);
@@ -353,7 +353,7 @@ C = cellComplex(R,P);
 S = ZZ[x];
 f = map(S,R,{});
 D = f**C;
-chainD = chainComplex D;
+chainD = complex D;
 assert(ring chainD === S);
 assert(HH_1(D)==0);
 assert(HH_2(D)==0);
@@ -432,7 +432,7 @@ e23 = newCell({v2,v3});
 e14 = newCell({v1,v4});
 f123 = newCell({e12,e13,e23});
 Delta = cellComplex(S, {f123,e14});
-C = chainComplex Delta;
+C = complex Delta;
 assert (dim Delta == 2);
 assert (length C == 3);
 ///
@@ -471,7 +471,7 @@ m = product(apply(numgens S, i -> S_i));
 G = apply(max X, l -> m//product(apply(l,i -> S_i)));
 H = hashTable apply(#G, i -> (j := F#i#0#0;((vertices P)_j,G_i)))
 C = cellComplex(S,P,Labels => H);
-Cres = (chainComplex C)[-1];
+Cres = (complex C)[-1];
 assert(betti (res B) == betti Cres);
 assert(HH_0 Cres == S^1/B);
 assert(HH_1 Cres == 0);
@@ -484,12 +484,12 @@ TEST ///
 R = QQ[x,y,z];
 I = monomialIdeal (x^2*z, x*y*z, y^2*z, x^3*y^5, x^4*y^4, x^5*y^3);
 H = hullComplex I;
-chainComplex H;
+complex H;
 assert(isMinimal H);
-assert(HH_(-1) chainComplex H == R^1/I);
-assert((HH_0 chainComplex H)==0);
+assert(HH_(-1) complex H == R^1/I);
+assert((HH_0 complex H)==0);
 H2 = hullComplex (3/2,I)
-assert((HH_0 chainComplex H2)!=0);
+assert((HH_0 complex H2)!=0);
 ///
 
 --isWellDefined test